suppose that the functions $g$ and $h$ are defined for all real numbers $x$ as follows.

\g(x) = x + 4\
\h(x) = 2x - 5\

find the following.

\(g \cdot h)(x) = \
\(g - h)(x) = \
\(g + h)(1) = \

Question

suppose that the functions $g$ and $h$ are defined for all real numbers $x$ as follows.

\g(x) = x + 4\
\h(x) = 2x - 5\

find the following.

\(g \cdot h)(x) = \
\(g - h)(x) = \
\(g + h)(1) = \

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Function Operations", "Function Multiplication", "Function Subtraction" ], "current_concepts": [ "Function Operations", "Function Multiplication", "Function Subtraction", "Function Addition" ] } ## Multiply the functions g(x) and h(x) $$ \begin{aligned} (g \cdot h)(x) &= g(x) \cdot h(x) \ &= (x + 4)(2x - 5) \ &= 2x^2 - 5x + 8x - 20 \ &= 2x^2 + 3x - 20 \end{aligned} $$ ## Subtract h(x) from g(x) $$ \begin{aligned} (g - h)(x) &= g(x) - h(x) \ &= (x + 4) - (2x - 5) \ &= x + 4 - 2x + 5 \ &= -x + 9 \end{aligned} $$ ## Evaluate the sum of g(1) and h(1) $$ \begin{aligned} (g + h)(1) &= g(1) + h(1) \ &= (1 + 4) + (2(1) - 5) \ &= 5 + (-3) \ &= 2 \end{aligned} $$ $$ \begin{aligned} (g \cdot h)(x) &= 2x^2 + 3x - 20 \ (g - h)(x) &= -x + 9 \ (g + h)(1) &= 2 \end{aligned} $$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Function Operations" ] }

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QUESTION IMAGE

Question

Explanation:

Multiply the functions g(x) and h(x)

Subtract h(x) from g(x)

Evaluate the sum of g(1) and h(1)

Answer: