Question

PLS ANSWER ASAP

Answer 1

9514 1404 393

Explanation:

Part 1.

The inverse of a function y = f(x) can be found by solving x = f(y) for y.

When we do that here, we find ...

  $x=f(y)\\\\x=\dfrac{y+a}{b}\\\\bx=y+a\\\\y=bx-a$

When we compare this to g(x), which we want to be the inverse of f(x), we see that ...

  cx -d = bx -a   ⇒   b=c, and d=a

We can choose a=d=1 and b=c=2 to make the two functions inverses:

  f(x) = (x +1)/2

  g(x) = 2x -1

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Part 2.

The inverse of f(x) is g(x) if f(g(x)) = x.

  f(g(x)) = ((2x -1) +1)/2 = 2x/1 = x . . . . . g is the inverse of f

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Part 3.

Same as Part 2, but in reverse.

  g(f(x)) = 2((x +1)/2) -1 = (x +1) -1 = x

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Part 4.

The attachment is a graph of the two functions and a table of values. The line y=x is the dashed orange line. You will notice that f(x) and g(x) are reflections of each other across that line.