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Convexity

Let fx=x2, gx...

Question

Let $f (x) = x^{2}, g (x) = 2^{x}$ . The number of integers in the solution set of $f o g (x) = g o f (x)$ is

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Solution

The correct option is C $2$
$f o g (x) = g o f (x) \Rightarrow f (2^{x}) = g (x^{2}) \Rightarrow {(2^{x})}^{2} = 2^{x^{2}} \Rightarrow 2 x = x^{2} ∴ x = 0, 2$

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Similar questions

Let $f (x) = x^{2}$ and $g (x) = 2 x + 1$ be two real functions. Find (f + g), (f - g) (x), (fg) (x) and $(\frac{f}{g}) (x)$

f (x) = x^{2}

g (x) = 2^{x}

f (x) = x^{2}

g (x) = 2^{x}

f o g (x) = g o f (x)

f (x) = x^{2}

g (x) = 2 x + 1

(f + g) (x), (f - g) (x), (f g) (x), \frac{f}{g} (x)

f : R \to R

g : R \to R

f (x) = x^{2} + 2 x - 3, g (x) = 3 x - 4

(g o f) (x) =

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