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QuestionGiven f(x)=−7−xf(x)=\sqrt{-7-x}, find: (a) f(p)f(p), (b) f(−r)f(-r), (c) f(m−8)f(m-8). Simplify each.

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=−7−xf(x)=\sqrt{-7-x} . We need to find f(p)f(p), f(−r)f(-r), and f(m−8)f(m-8)

STEP 2

The function f(x)f(x) is defined as −7−x\sqrt{-7-x}. To find f(p)f(p), we replace xx with pp in the function.
f(p)=−7−pf(p)=\sqrt{-7-p}

STEP 3

implify the function f(p)f(p).
f(p)=−7−pf(p)=\sqrt{-7-p}

STEP 4

To find f(−r)f(-r), we replace xx with −r-r in the function.
f(−r)=−7−(−r)f(-r)=\sqrt{-7-(-r)}

STEP 5

implify the function f(−r)f(-r).
f(−r)=−7+rf(-r)=\sqrt{-7+r}

STEP 6

To find f(m−8)f(m-8), we replace xx with m−8m-8 in the function.
f(m−8)=−−(m−8)f(m-8)=\sqrt{--(m-8)}

STEP 7

implify the function f(m−)f(m-).
f(m−)=−7−m+f(m-)=\sqrt{-7-m+}

STEP 8

Further simplify the function f(m−8)f(m-8).
f(m−8)=1−mf(m-8)=\sqrt{1-m}So, f(p)=−7−pf(p)=\sqrt{-7-p}, f(−r)=−7+rf(-r)=\sqrt{-7+r}, and f(m−8)=1−mf(m-8)=\sqrt{1-m}.

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