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Math  /  Algebra

Question4. f(x)=−5x+10g(x)=−x−7f(x)=-5 x+10 \quad g(x)=-x-7 Find h(x)=f(x)+g(x)h(x)=f(x)+g(x).

Studdy Solution

STEP 1

1. We are given two functions, f(x)=−5x+10 f(x) = -5x + 10 and g(x)=−x−7 g(x) = -x - 7 .
2. We need to find the function h(x) h(x) which is the sum of f(x) f(x) and g(x) g(x) .
3. The operations involved are basic algebraic addition of functions.

STEP 2

1. Write down the expressions for f(x) f(x) and g(x) g(x) .
2. Add the expressions for f(x) f(x) and g(x) g(x) to find h(x) h(x) .
3. Simplify the expression for h(x) h(x) .

STEP 3

Write down the expressions for the given functions:
f(x)=−5x+10 f(x) = -5x + 10 g(x)=−x−7 g(x) = -x - 7

STEP 4

Add the expressions for f(x) f(x) and g(x) g(x) :
h(x)=f(x)+g(x)=(−5x+10)+(−x−7) h(x) = f(x) + g(x) = (-5x + 10) + (-x - 7)

STEP 5

Combine like terms:
h(x)=(−5x−x)+(10−7) h(x) = (-5x - x) + (10 - 7)

STEP 6

Simplify the expression:
h(x)=−6x+3 h(x) = -6x + 3

STEP 7

The function h(x) h(x) is now simplified to:
h(x)=−6x+3 h(x) = -6x + 3

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