Questions: Given that f(x)=8x-4 and g(x)=1-x^2, calculate (a) f(g(0))= (b) g(f(0))=

Given that f(x)=8x-4 and g(x)=1-x^2, calculate (a) f(g(0))= (b) g(f(0))=
Transcript text: Given that $f(x)=8 x-4$ and $g(x)=1-x^{2}$, calculate (a) $f(g(0))=$ $\square$ (b) $g(f(0))=$ $\square$
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Solution

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Solution Steps

Step 1: Calculate \( g(0) \)

Given \( g(x) = 1 - x^{2} \), substitute \( x = 0 \): \[ g(0) = 1 - (0)^{2} = 1 - 0 = 1 \]

Step 2: Calculate \( f(g(0)) \)

Now, substitute \( g(0) = 1 \) into \( f(x) = 8x - 4 \): \[ f(g(0)) = f(1) = 8(1) - 4 = 8 - 4 = 4 \]

Step 3: Calculate \( f(0) \)

Given \( f(x) = 8x - 4 \), substitute \( x = 0 \): \[ f(0) = 8(0) - 4 = 0 - 4 = -4 \]

Step 4: Calculate \( g(f(0)) \)

Now, substitute \( f(0) = -4 \) into \( g(x) = 1 - x^{2} \): \[ g(f(0)) = g(-4) = 1 - (-4)^{2} = 1 - 16 = -15 \]

(a) \( f(g(0)) = \boxed{4} \)

(b) \( g(f(0)) = \boxed{-15} \)

Final Answer

(a) \( f(g(0)) = \boxed{4} \)

(b) \( g(f(0)) = \boxed{-15} \)

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