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Math  /  Algebra

QuestionCONCAVII
Worksheet A: (Topic 2.7) Composition of Function Directions: Use the given functions below to evalua f(x)=4x−5g(x)=x2−2x+4f(x)=4 x-5 \quad g(x)=x^{2}-2 x+4
1. f(g(1))=f(g(1))=

Studdy Solution

STEP 1

1. We are given two functions: f(x)=4x−5 f(x) = 4x - 5 and g(x)=x2−2x+4 g(x) = x^2 - 2x + 4 .
2. We need to evaluate the composition of functions f(g(1)) f(g(1)) .

STEP 2

1. Evaluate the inner function g(1) g(1) .
2. Substitute the result from Step 1 into the outer function f(x) f(x) .
3. Simplify to find f(g(1)) f(g(1)) .

STEP 3

Evaluate the inner function g(x) g(x) at x=1 x = 1 :
g(1)=(1)2−2(1)+4 g(1) = (1)^2 - 2(1) + 4

STEP 4

Simplify the expression for g(1) g(1) :
g(1)=1−2+4 g(1) = 1 - 2 + 4 g(1)=3 g(1) = 3

STEP 5

Substitute g(1)=3 g(1) = 3 into the outer function f(x) f(x) :
f(g(1))=f(3)=4(3)−5 f(g(1)) = f(3) = 4(3) - 5

STEP 6

Simplify the expression for f(3) f(3) :
f(3)=12−5 f(3) = 12 - 5 f(3)=7 f(3) = 7
The value of f(g(1)) f(g(1)) is:
7 \boxed{7}

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