Question

it's not a really a question but how to solve these types of questions
Let f(x) = 9x − 2 and g(x) = −x + 3. Find f(g(x)).

Let f(x) = 2x + 2. Solve f−1(x) when x = 4.

Let f(x) = x + 8 and g(x) = x2 − 6x − 7. Find f(g(2)).

Let f(x) = x2 − 8x + 5. Find f(−1).

Answer 1

1. 9(-x+3) - 2
3.[ (2)2 - 6(2) - 7] + 8
4.(-1)2 - 8(-1) + 5

Answer 2

Answer:

Part 1) $f(x) = 9x- 2$  and $g(x) = -x + 3$

Find f(g(x)).

$f(x) = 9x- 2$

Substitute value of g(x) in place of x

$f(g(x)) = 9(-x+3)- 2$

$f(g(x)) = -9x+27- 2$

$f(g(x)) = -9x+25$

So, $f(g(x)) = -9x+25$

Part 2) $f(x) = 2x + 2$

$y = 2x + 2$

Replace y with x and x with y

$x = 2y + 2$

Find y

$\frac{x-2}{2} = y$

So, $f^{-1}(x)=\frac{x-2}{2}$

Substitute x = 4

$f^{-1}(4)=\frac{4-2}{2}$

$f^{-1}(4)=1$

Part 3) $f(x) = x + 8$ and $g(x) = x^2- 6x-7$

$f(x) = x + 8$

Substitute value of g(x) in place of x

$f(g(x)) =x^2- 6x-7 + 8$

$f(g(x)) =x^2- 6x+1$

Substitute x = 2

$f(g(x)) =2^2- 6(2)+1$

$f(g(x)) =4- 12+1$

$f(g(x)) =-7$

Part 4) $f(x) = x^2-8x + 5$

Substitute x = -1

$f(-1) = (-1)^2-8(-1) + 5$

$f(-1) =14$