Question

f:R—>R, f(x)=x², g: R—>R,g(x)=2ˣ, then { x | (fog)(x)=(gof)(x)}=.....,Select Proper option from the given options.
(a) {0}
(b) {0,1}
(c) R
(d) {0,2}

Answer 1

f : R -----> R , f(x) = x² ,
g : R -----> R , g(x) = 2^x

we have to find the value of x for which (fog)(x) = (gof)(x)

first of all, we have to find (fog)(x) = f(g(x))
= f(2^x) = {2^x}² = 2^2x

again,find (gof)(x) = g(f(x)) = g(x²)
= 2^x²

now, (fog)(x) = (gof)(x)
2^2x = 2^x²
=> 2x = x²
=> x² - 2x = 0
=> x(x - 2) = 0
=> x = 0, 2

hence, option (d) is correct.