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The domain of the function $\mathrm{f}(\mathrm{x})$ is $[-2,14]$ and the range is $(-\infty, 19]$ . Using interval notation find the domain and range of $g(x)=f(-x)$ .
Answer Attempt 1 out of 3
Domain: $\square$ Range: $\square$

Studdy Solution

STEP 1

1. The function $f(x)$ has a given domain and range.
2. The transformation $g(x) = f(-x)$ involves reflecting the function across the y-axis.
3. Reflecting across the y-axis affects the domain but not the range.

STEP 2

1. Determine the domain of $g(x) = f(-x)$ .
2. Determine the range of $g(x) = f(-x)$ .

STEP 3

The domain of $f(x)$ is given as $[-2, 14]$ . When we consider $g(x) = f(-x)$ , we reflect the domain across the y-axis. This means we take the negative of each endpoint of the interval:
Original domain: $[-2, 14]$
Reflecting across the y-axis, we get:
$[-14, 2]$

STEP 4

The range of $f(x)$ is given as $(-\infty, 19]$ . The transformation $g(x) = f(-x)$ does not affect the range because it is a horizontal reflection. Therefore, the range remains the same:
$(-\infty, 19]$
The domain of $g(x) = f(-x)$ is $[-14, 2]$ and the range is $(- \infty, 19]$ .
Domain: $[-14, 2]$ Range: $(- \infty, 19]$

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