Question

If f(x) = 2x + 7 and g(x) = x² + 7, x ∈ R, then what are the values of x for which f ∘ g(x) = 25?
1. -1, 1
2. -2, 2
3. \(-\sqrt{2}, \sqrt{2}\)
4. None of the above

Answer 1

Correct Answer - Option 3 : \(-\sqrt{2}, \sqrt{2}\)

Concept:

Composition of function: Let f, and g be any functions then, f ∘ g(x) = f[g(x)]

Calculations:

Given, f(x) = 2x + 7 and g(x) = x2 + 7, x ∈ R

and f ∘ g(x) = 25

⇒f[g(x)] = 25

⇒ f(x2 + 7) = 25

⇒ 2(x2 + 7) + 7 = 25

⇒ 2x2 + 14 + 7 = 25

⇒ 2x2 = 4

⇒ x2 = 2

⇒ x = \(\rm -\sqrt2, \sqrt2\)