Answer:
[tex]f {}^{ - 1} (x)[/tex]
means the inverse function of
[tex]f(x)[/tex]
To do that, we just do the following steps.
1. Set up equation
[tex]f(x) = 2x + 2[/tex]
Remember Ruler Notation, that f(x)=y
[tex]y = 2x + 2[/tex]
Swap x and y
[tex]x = 2y + 2[/tex]
Solve for y
[tex]x - 2 = 2y[/tex]
[tex] \frac{1}{2} x - 1 = y[/tex]
So we found our inverse function, now we just plug in 4 for x
[tex]( \frac{1}{2} )(4) - 1 = y[/tex]
[tex]2 - 1 = y[/tex]
[tex]1 = y[/tex]
Option 4 is the answer.
For question 6, plug in 2 for x in function g
We get
[tex](2) {}^{2} - 6(2) - 7[/tex]
[tex] = - 15[/tex]
Now, we plug in -15 for f.
[tex] - 15 + 8[/tex]
[tex] = - 7[/tex]
Option 1 is the answer.
For question 7, plug in g(x) for x in f(x).
[tex]9( - x + 3) - 2 = - 9x + 27 - 2 = - 9x + 25[/tex]
Option 1 is the answer.
We are given
[tex] {x}^{2} - 16 = y[/tex]
[tex] {y}^{2} - 16 = x[/tex]
[tex]y {}^{2} = x + 16[/tex]
[tex]y = \sqrt{x + 16} [/tex]
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.
[tex]( - 1) {}^{2} - (7)( - 1) - 9 = - 1[/tex]
Now, plug that in for x in f(x).
[tex] - 1 - 2 = - 3[/tex]
Option 1 is the answer.
Next, just compose again.
[tex] - 4(10x - 6) + 7 = - 40x + 24 + 7 = - 40x + 31[/tex]
Option 4 is the answer.
[tex]y = 2x - 6[/tex]
[tex]y + 6 = 2x[/tex]
[tex]x = \frac{1}{2} y + 3[/tex]
[tex]y = \frac{1}{2} x + 3[/tex]
Plug in 2
[tex]y = ( \frac{1}{2} )2 + 3[/tex]
[tex]y = 4[/tex]
First Option is answer.
