Question

01.02 Introduction to Functions... I need help

I'm usually the one helping everyone else but now I need help... anyway, I want answers WITH explanations. I'm trying to understand this not just to get answers. Any irrelevant answers by people just trying to harvest points WILL BE immediately flagged. The best answer will get Brainliest :) Thank you!

Answer 1

Answer:

$f {}^{ - 1} (x)$

means the inverse function of

$f(x)$

To do that, we just do the following steps.

1. Set up equation

$f(x) = 2x + 2$

Remember Ruler Notation, that f(x)=y

$y = 2x + 2$

Swap x and y

$x = 2y + 2$

Solve for y

$x - 2 = 2y$

$\frac{1}{2} x - 1 = y$

So we found our inverse function, now we just plug in 4 for x

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

$2 - 1 = y$

$1 = y$

Option 4 is the answer.

For question 6, plug in 2 for x in function g

We get

$(2) {}^{2} - 6(2) - 7$

$= - 15$

Now, we plug in -15 for f.

$- 15 + 8$

$= - 7$

Option 1 is the answer.

For question 7, plug in g(x) for x in f(x).

$9( - x + 3) - 2 = - 9x + 27 - 2 = - 9x + 25$

Option 1 is the answer.

We are given

${x}^{2} - 16 = y$

${y}^{2} - 16 = x$

$y {}^{2} = x + 16$

$y = \sqrt{x + 16}$

Option 4 is the answer. Rember square roots give two answers, a positive and negative unless we take the only the positive answer.

Plug in -1 in g.

$( - 1) {}^{2} - (7)( - 1) - 9 = - 1$

Now, plug that in for x in f(x).

$- 1 - 2 = - 3$

Option 1 is the answer.

Next, just compose again.

$- 4(10x - 6) + 7 = - 40x + 24 + 7 = - 40x + 31$

Option 4 is the answer.

$y = 2x - 6$

$y + 6 = 2x$

$x = \frac{1}{2} y + 3$

$y = \frac{1}{2} x + 3$

Plug in 2

$y = ( \frac{1}{2} )2 + 3$

$y = 4$

First Option is answer.