Inverse function

Question

a. Find the inverse function of g(x)= (4x^5-2)/7

b. Find g(g^-1 (x)) What does this tell you?

(The ^-1 means 'inverse' idk how to put it on here lol, sorry)

Answer 1

a. Find the inverse function of g(x)= (4x^5-2)/7

b. Find g(g^-1 (x)) What does this tell you?

For par a

y = g(x ) =( 4X⁵ -2)/7

Interchange X and Y

X = ( 4Y⁵ -2 ) /7

Get Y from here

4Y⁵ - 2 = 7x

4 Y⁵ = 7X +2

Y⁵ = (7X +2)/4

Y = g-¹(X) = inverse of g(X)

= (7X +2)^1/5 / (4)^1/5

Part b

g(g^-1 (x) simply means g(X)

or g( g^-1 (X) = g(X)