# If f(x) = 2x and g(x) = 5x, calculate f(g(

## Answers

F(x)=2x

G(x)=5x

F(g(x))=?

Start with G(x)=5x

Then plug that in for x in f(x)=2x

Therefore getting f(g(x))=2(5x)

Simplify

F(g(x))=10x

[tex]f(x)=2x-3x[/tex] and [tex]g(x)=-5x-1[/tex]

For [tex]f(x)=2x-3x[/tex] :

[tex]x=-5[/tex]

[tex]f(-5)=2x-3x\\f(-5)=2(-5)-3(-5)\\f(-5)=-10+15\\f(-5)=5[/tex]

For [tex]g(x)=-5x-1[/tex]:

[tex]x=5[/tex]

[tex]g(5)=-5x-1\\g(5)=-5(5)-1\\g(5)=-25-1\\g(5)=-26[/tex]

Asked to find h(4). Hence, we don not need f(x) and g(x).

Substitute x=4 in h(x).

so, h(4) = 7*(4)^2 - 8 => 112 - 8 => 104

hope it helps.

F(x)=2x^2

Step-by-step explanation:

Basically, a quadratic function has x^2 in it (standard form ax^2+bx+c with non-zero a). The others have x^3, -x, x^4, etc., which clearly are NOT x^2.

h(x)=[tex]-10x^{2}+40x[/tex]

Step-by-step explanation:

given ,[tex]f(x)=2x-8[/tex]

given, [tex]g(x)=-5x[/tex]

Given that [tex]h(x)=f(x)g(x)[/tex]

Let [tex]t_{1}[/tex] be [tex]k_{1}x^{n_{1}}[/tex] where [tex]k_{1} \text{ and } n_{1} \text{ are constants}[/tex]

Let [tex]t_{2}[/tex] be [tex]k_{2}x^{n_{2}}[/tex] where [tex]k_{2} \text{ and } n_{2} \text{ are constants}[/tex]

We know that [tex]t_{1}\times t_{2}=k1\times x^{n_{1}}\times k2\times x^{n_{2}}[/tex]=[tex]k_1k_2x^{n_{1}+n_{2}}[/tex]

So,[tex]h(x)=(2x-8)(-5x)[/tex]=[tex]-10x^{2}+40x[/tex]

hx = f(x) - g(x)

f(x) = -2x + 17

g(x) = -5x - 10

You can substitute/plug in (-2x + 17) into "f(x)" since f(x) = -2x + 17, and you can substitute (-5x - 10) into "g(x)" since g(x) = -5x - 10.

h(x) = f(x) - g(x)

h(x) = (-2x + 17) - (-5x - 10) Now simplify, first distribute -1 into (-5x - 10)

h(x) = (-2x + 17) - (-1)5x - (-1)10 (two negative signs cancel each other out and become positive)

h(x) = -2x + 17 + 5x + 10 Combine like terms (terms that have the same variable and power/exponent)

h(x) = 3x + 27

Step-by-step explanation:

The domain and target set of functions f and g given is expressed as;

f(x) = 2x+3 an g(x) = 5x+7 on R. To calculate the given functions, the following steps must be followed.

a) f◦g

f◦g = f(g(x)]) = f(5x+7)

To solve for the function f(5x+7), the variable x in f(x) will be replaced with 5x+7 as shown;

f(x) = 2x+3

f(5x+7) = 2(5x+7)+3

f(5x+7) = 10x+14+3

f(5x+7) = 10x+17

Therefore the function f◦g is equivalent to 10x+17

b) For the composite function g◦f

g◦f = g(f(x)])

g(f(x)) = g(2x+3))

To drive the functon g(2x+3), the variable x in g(x) will be replaced with 2x+3 as shown;

g(x) = 5x+7

g(2x+3) = 5(2x+3)+7

g(2x+3) = 10x+15+7

g(2x+3) = 10x+22

This shoes that the composite function g◦f = 10x+22

c) To get the inverse of the composite function f◦g i.e (f◦g)⁻¹

Given (f◦g) = 10x+17

To find the inverse, first we will replace (f◦g) with variable y to have;

y = 10x+17

Then we will interchange variable y for x:

x = 10y+17

We will then make y the subject of the formula;

10y = x-17

y = (x-17)/10

Hence (f◦g)⁻¹ = (x-17)/10

d) For the function f⁻¹◦g⁻¹

First we need to calculate for the inverse of function f(x) and g(x) as shown:

For f⁻¹(x):

Given f(x)= 2x+3

To find the inverse, first we will replace f(x) with variable y to have;

y = 2x+3

Then we will interchange variable y for x:

x = 2y+3

We will then make y the subject of the formula;

2y = x-3

y = (x-3)/2

f⁻¹(x) = (x-3)/2

Similarly for the function g⁻¹(x):

Given g(x)= 5x+7

To find the inverse, first we will replace g(x) with variable y to have;

y = 5x+7

Then we will interchange variable y for x:

x = 5y+7

We will then make y the subject of the formula;

5y = x-7

y = (x-7)/5

g⁻¹(x) = (x-7)/5

Now to get f⁻¹◦g⁻¹

f⁻¹◦g⁻¹= f⁻¹(g⁻¹(x))

f⁻¹(g⁻¹(x)) = f⁻¹((x-7)/5)

Since f⁻¹(x) = (x-3)/2

f⁻¹((x-7)/5) = [(x-7)/5)-3]/2

= [(x-7)-15/5]/2

= [(x-7-15)/5]/2

= [x-22/5]/2

= (x-22)/10

Hence f⁻¹◦g⁻¹= (x-22)/10

e) For the composite function g⁻¹◦f⁻¹

g⁻¹◦f⁻¹= g⁻¹[f⁻¹x)]

g⁻¹[f⁻¹(x)] = g⁻¹((x-3)/2)

Since g⁻¹(x) = (x-7)/5

g⁻¹(x-3/2) = [(x-3/2)-7]/5

= [(x-3)-14)/2]/5

= [(x-17)/2]/5

= (x-17)/10

Therefore the composite function g⁻¹◦f⁻¹= (x-17)/10

Step-by-step explanation:

f(-5)=-10+15=5

g(5)=25-1=24

Step-by-step explanation:

F(x) = 2x + 6

G(x) = - 5x - 9

product of F and G the product is the result of multiplication

(2x + 6)(-5x - 9) =

-10x^2 - 18x - 30x - 54 =

-10x^2 - 48x - 54 <

Step-by-step explanation:

Given the domain and target set of functions f and g expressed as;

f(x) = 2x+3 an g(x) = 5x+7 we are to find the following;

a) f◦g

f◦g = f[g(x)]

f[g(x)] = f[5x+7]

To get f(5x+7), we will replace the variable x in f(x) with 5x+7 as shown;

f(x) = 2x+3

f(5x+7) = 2(5x+7)+3

f(5x+7) = 10x+14+3

f(5x+7) = 10x+17

Hence f◦g = 10x+17

b) g◦f

g◦f = g[f(x)]

g[f(x)] = g[2x+3]

To get g(2x+3), we will replace the variable x in g(x) with 2x+3 as shown;

g(x) = 5x+7

g(2x+3) = 5(2x+3)+7

g(2x+3) = 10x+15+7

g(2x+3) = 10x+22

Hence g◦f = 10x+22

c) For (f◦g)−1 (inverse of (f◦g))

Given (f◦g) = 10x+17

To find the inverse, first we will replace (f◦g) with variable y to have;

y = 10x+17

Then we will interchange variable y for x:

x = 10y+17

We will then make y the subject of the formula;

10y = x-17

y = x-17/10

Hence the inverse of the function

(f◦g)−1 = (x-17)/10

d) For the function f−1◦g−1

We need to get the inverse of function f(x) and g(x) first.

For f-1(x):

Given f(x)= 2x+3

To find the inverse, first we will replace f(x) with variable y to have;

y = 2x+3

Then we will interchange variable y for x:

x = 2y+3

We will then make y the subject of the formula;

2y = x-3

y = x-3/2

Hence the inverse of the function

f-1(x) = (x-3)/2

For g-1(x):

Given g(x)= 5x+7

To find the inverse, first we will replace g(x) with variable y to have;

y = 5x+7

Then we will interchange variable y for x:

x = 5y+7

We will then make y the subject of the formula;

5y = x-7

y = x-7/5

Hence the inverse of the function

g-1(x) = (x-7)/5

Now to get )f−1◦g−1

f−1◦g−1 = f-1[g-1(x)]

f-1[g-1(x)] = f-1(x-7/5)

Since f-1(x) = x-3/2

f-1(x-7/5) = [(x-7/5)-3]/2

= [(x-7)-15/5]/2

= [(x-7-15)/5]/2

= [x-22/5]/2

= (x-22)/10

Hence f−1◦g−1 = (x-22)/10

e) For the composite function g−1◦f−1

g−1◦f−1 = g-1[f-1(x)]

g-1[f-1(x)] = g-1(x-3/2)

Since g-1(x) = x-7/5

g-1(x-3/2) = [(x-3/2)-7]/5

= [(x-3)-14)/2]/5

= [(x-17)/2]/5

= x-17/10

Hence g-1◦f-1 = (x-17)/10