Question

See instructions on photo to find a) f(10) b) g(-8) c) g(f(-4)) d) f(g(-2))

Answer 1

Given:

`\begin{gathered} f(x)=x^2-2 \\ g(x)\text{ = 2x + 1} \end{gathered}`

To find the value of the function at any x-value, we simply substitute the x-value into the function expression.

f(10):

`\begin{gathered} f(10)=(10)^2-2 \\ =\text{ 100 - 2} \\ =\text{ 98} \end{gathered}`

g(-8):

`\begin{gathered} g(-8)\text{ = 2(-8) + 1} \\ =\text{ -16 + 1} \\ =\text{ -15} \end{gathered}`

g(f(-4):

We have to find f(-4) first, and then substitute the solution into g(x)

`\begin{gathered} f(-4)=(-4)^2-2 \\ =\text{ 16 - 2} \\ =\text{ 14} \\ g(f(-4))\text{ = g(14)} \\ g(14)\text{ = 2(14) + 1} \\ =28\text{ + 1} \\ =\text{ 29} \end{gathered}`

d) f(g(-2)):

`\begin{gathered} g(-2)=\text{ 2(-2) + 1} \\ =\text{ -4 + 1} \\ =\text{ -3} \\ f(g(-2))\text{ = f(-3)} \\ f(-3)=(-3)^2-2 \\ =\text{ 9 - 2} \\ =\text{ 7} \end{gathered}`

Answers:

(a) f(10)= 98

(b) g(-8)= -15

(c) g(f(-4)) =29

(d) f(g(-2)) = 7