Question

Verify that f and g are inverse functions. f(x)=5x^2-2, x>=0, g(x)=(x+2/5)^1/2

Answer 1

let f(x)=y=5x^2-2
now for finding inverse first find value of x in term of y and after that switch x and y

Answer 2

y=5x^2-2
y+2=5x^2
(y+2)/5=x^1/2
\[x=\sqrt{\frac{ y+2 }{ 5 }}\]

Answer 3

now switch x and y
\[y=\sqrt{\frac{ x+2 }{ 5 }}\]
this is inverse of f(x) or it is g(x) hence g(x) is inverse of f(x)

Answer 4

okay got it

Answer 5

then for the g(x)?

Answer 6

what would that be = to?

Answer 7

what is the x>=0 all about..

Answer 8

g(x)=y lol

Answer 9

if we not consider x>=0 then before sqrt + and - sign will be there
but x>=0 so our ans will be positive so remove negative sign

Answer 10

similarly find for g(x)