Question

Let f(x) be the function defined below, for the interval -1 < x < 1.

f(x) = 7 + x^2 + tan(pi*x/2)

(a) find f-1(7)
(b) find f(f-1(4))

Note: f-1 stands for inverse.

Answer 1

How would I go about with doing this?

Answer 2

We have to realize or work with the definition of inverse in mind. Keeping that in mind, realize that if the f^-1(7) then f(y)=7. Thus we have to find the value that makes the original equation 7. Namely we have to solve:
7+x^2+tan(pi*x/2)=7

Answer 3

That's exactly what I came up with in the beginning. Only right after that, I realized that I don't know how to proceed from there.

Answer 4

subtract 7 from both sides

Answer 5

ok

Answer 6

then, its acutally quite comical how we can , just using out eyes realize when x^2 and the tan fucntion are 0

Answer 7

im sorry but im not seeing it unfortunately.

Answer 8

come on man, just look at it:

x^2+tan(pi*x/2)=0

When is x^2 0?
When is tan(pix/2) 0?

Answer 9

at x = 0, at x^2 = 0. at x = 0, tan(pi*x/2) also equals 0.

Answer 10

so the f^-1(7)=0

Answer 11

So how would part b work?

Answer 12

simply: f(g(x)=x
Where g(x) is the inverse

Answer 13

you just got schooled

Answer 14

We don't have the g(x)

Answer 15

do i have to spell it out, i guess so:

f(f^-1(4))=4

Answer 16

Aw man you shouldn't have. Ok thanks anyways.