Question

Which of the following statements have the same result? Explain each step in solving each one.

I.f(2) when f(x) = 3x + 2
II.f-1(3) when f(x) = 2 x minus 7, all over 3
III.2y + 14 = 4y - 2

Answer 1

First: f(2) is same as f(x=2) so all we have to do is to express x=2 in f(x)
f(2) = 3*2 + 2 = 8

Second
f^(-1) (3) is inverse function. first we solve f(x) for x.
let f(x) be equal to some variable m
m = (2x -7)/3
3m = 2x - 7
2x = 3m + 7
x = (3m + 7)/3
now we write:
f^-1(x) = (3x + 7)/3

x=3
f^-1(3) = 16/3

Third
2y + 14 = 4y - 2
we just solve for y
2y = 16
y = 8

Now we take that f(x) = y because we both write to be the functions of x

that means that First and third have same result.