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Math  /  Algebra

QuestionGiven that f(x)=4x+5f(x)=4 x+5 and g(x)=5−x2g(x)=5-x^{2}, calculate (a) f(g(0))=f(g(0))= □\square (b) g(f(0))=g(f(0))= □\square Question Help: Video 1 Video 2

Studdy Solution

STEP 1

1. We are given two functions: f(x)=4x+5 f(x) = 4x + 5 and g(x)=5−x2 g(x) = 5 - x^2 .
2. We need to calculate f(g(0)) f(g(0)) .
3. We need to calculate g(f(0)) g(f(0)) .

STEP 2

1. Calculate g(0) g(0) .
2. Substitute the result from Step 1 into f(x) f(x) to find f(g(0)) f(g(0)) .
3. Calculate f(0) f(0) .
4. Substitute the result from Step 3 into g(x) g(x) to find g(f(0)) g(f(0)) .

STEP 3

Calculate g(0) g(0) by substituting x=0 x = 0 into g(x) g(x) :
g(0)=5−(0)2 g(0) = 5 - (0)^2 g(0)=5−0 g(0) = 5 - 0 g(0)=5 g(0) = 5

STEP 4

Substitute the result from Step 1 into f(x) f(x) to find f(g(0)) f(g(0)) :
f(g(0))=f(5) f(g(0)) = f(5) f(5)=4(5)+5 f(5) = 4(5) + 5 f(5)=20+5 f(5) = 20 + 5 f(5)=25 f(5) = 25
So, f(g(0))=25 f(g(0)) = 25 .

STEP 5

Calculate f(0) f(0) by substituting x=0 x = 0 into f(x) f(x) :
f(0)=4(0)+5 f(0) = 4(0) + 5 f(0)=0+5 f(0) = 0 + 5 f(0)=5 f(0) = 5

STEP 6

Substitute the result from Step 3 into g(x) g(x) to find g(f(0)) g(f(0)) :
g(f(0))=g(5) g(f(0)) = g(5) g(5)=5−(5)2 g(5) = 5 - (5)^2 g(5)=5−25 g(5) = 5 - 25 g(5)=−20 g(5) = -20
So, g(f(0))=−20 g(f(0)) = -20 .
The solutions are: (a) f(g(0))=25 f(g(0)) = 25 (b) g(f(0))=−20 g(f(0)) = -20

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