Question

Let f and g be functions from R to R defined as

\( f(x) = \begin{cases} 7x^2 + x - 8, & x \le 1 \\ 4x + 5, & 1 < x \le 7 \\ 8x + 3, & x > 7 \end{cases} \)

\( g(x) = \begin{cases} |x|, & x < -3 \\ 0, & -3 \le x < 2 \\ x^2 + 4, & x \ge 2 \end{cases} \)

Then

• A. \((f\circ g)(-3)=8\)
• B. \((f\circ g)(9)=683\)
• C. \((g\circ f)(0)=-8\)
• D. \((g\circ f)(6)=427\)

Hint:

For composite functions, always evaluate the inner function first, then apply the outer function using the correct case.

Answer 1

The Correct Option is B

Step 1: Evaluate option (B). g(9)=9²+4=85 (f∘ g)(9)=f(85) Since 85>7, f(85)=8(85)+3=680+3=683 Step 2: Hence, option (B) is correct. (Other options give incorrect values on substitution.)