Question

if \\(g(x) = \frac{x+1}{x-2}\\) and \\(h(x) = 4 - x\\), what is the value of \\((g \circ h)(-3)\\)?

• \\(\frac{8}{5}\\)
• \\(\frac{5}{2}\\)
• \\(\frac{15}{2}\\)
• \\(\frac{18}{5}\\)

Explanation:

Evaluate the inner function h(-3)

$$ h(-3) = 4 - (-3) = 4 + 3 = 7 $$

Evaluate the outer function g(7)

$$ g(7) = \frac{7 + 1}{7 - 2} = \frac{8}{5} $$

Combine results for the composite value

$$ (g \circ h)(-3) = g(h(-3)) = g(7) = \frac{8}{5} $$

Answer:

• (A) \(\frac{8}{5}\) (Correct answer)
• (B) \(\frac{5}{2}\)
• (C) \(\frac{15}{2}\)
• (D) \(\frac{18}{5}\)