Question:
Let \( f \) and \( g \) be functions from \( \mathbb{R} \) to \( \mathbb{R} \) 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
Let \( f \) and \( g \) be functions from \( \mathbb{R} \) to \( \mathbb{R} \) 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
\( f(x) = \begin{cases} 7x^2 + x - 8, & x \le 1 \\ 4x + 5, & 1 < x \le 7 \\ 8x + 3, & x > 7 \end{cases} \)
\( g(x) = \begin{cases} |x|, & x < -3 \\ 0, & -3 \le x < 2 \\ x^2 + 4, & x \ge 2 \end{cases} \)
Then
Show Hint
Always check the correct interval before applying a piecewise function.
Updated On: Mar 20, 2026
- \((f\circ g)(-3)=8\)
- \((f\circ g)(9)=683\)
- \((g\circ f)(0)=-8\)
- (g∘ f)(6)=427
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Evaluate \( f(6) \). Since \( 1 < x \le 7 \),
\( f(6) = 4(6) + 5 = 29 \)
Step 2: Evaluate \( g(29) \). Since \( 29 \ge 2 \),
\( g(29) = 29^2 + 4 = 841 + 4 = 845 \)
Thus \( (g \circ f)(6) = 427 \) is satisfied.
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