Let f(x)=(2x-5)/(,x+3,) and g(x)=x^2+1. Find the value of (gcirc f)(2).

Let $f (x) = \frac{2 x - 5}{, x + 3 ,}$ and $g (x) = x^{2} + 1$ . Find the value of $(g c i r c f) (2)$ .

medium MCQ 4 marks Class 12 · Mathematics · Relations and Functions

Answer

\frac{26}{25}

The correct answer is A) $\frac{26}{25}$ — Thus $(g c i r c f) (2) = \frac{26}{25}$ .

Compute $f (2) = \frac{2 ( 2 ) - 5}{2 + 3} = \frac{- 1}{5} = - \frac{1}{5}$ .
Evaluate $g$ at this value: $g! (- \frac{1}{5}) = (- \frac{1}{5})^{2} + 1 = \frac{1}{25} + 1 = \frac{26}{25}$ .
Thus $(g c i r c f) (2) = \frac{26}{25}$ .

Common mistake: Using wrong order of composition

Concept tested: Function composition