Let `f(x)=x^2` and `g(x)=2^x` . Then the solution set of the equation `fog(x)=gof(x)` is `(a)R` (b) {0} (c) {0, 2} (d) none of these

Options

A. R
B. {0}
C. {0,2}
D. None of these

Answer

C

Explanation

We have
`f(x)=x^(2) and g(x)=2^(x)`
`therefore fog(x)=g of (x)`
`Rightarrow f(g(x))=g(f(x))`
`Rightarrow f(2^(x))=g(x^(2))`
`Rightarrow (2^(x))^(2)=2^(x^(2))`
`Rightarrow 2^(2x)=2^(x^(2))Rightarrow 2x=x^(2) Rightarrow x(2-x)=0Rightarrow x=0,2`