Question

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1.) Given f(x) = x3 + 1 and g(x) = −x + 1 what is the value of (fg)(−4)?

A.) 315

B.) -315

C.) 225

D.) -225

2.) Given f(x) = x2 + 1 and g(x) = 3x, find (fg)(x).

A.) (fg)(x) = x2 + 3x + 1

B.) (fg)(x) = 3x^2 + 1

C.) (fg)(x) = 3x^3 + 1

D.) (fg)(x) = 3x^3 + 3x

Answer 1

Answer: FOR NUMBER 2 (B)

Step-by-step explanation:

2. (fg)(x) = f (3x)

= (3x)2 + 1 = 3x^2 + 1 —> B

Answer 2

The value of (fg)(-4) using the provided functions is not listed among the provided options; the correct value is A (315).

For the second part, the composition (fg)(x) results in (fg)(x) = 3x^2 + 1, which corresponds to answer B.

Step-by-step explanation:

The correct answer is (A) 315.

- Use the formula for the product of two functions, \((fg)(x) = f(x) \cdot g(x)\).

- Substitute \(x = -4\) into the expressions for \(f(x)\) and \(g(x)\) to find \(f(-4)\) and \(g(-4)\).

- Multiply \(f(-4)\) and \(g(-4)\) to get the value of \((fg)(-4)\).

(2) Expression for (fg)(x):

The correct answer is (B) (fg)(x) = 3x^2 + 1.

- Use the formula for the product of two functions, \((fg)(x) = f(x) \cdot g(x)\).

- Substitute \(f(x) = x^2 + 1\) and \(g(x) = 3x\) into the product expression.

- Multiply \(x^2 + 1\) and \(3x\) to get the final expression for \((fg)(x)\).

In question 1, evaluating \((fg)(-4)\) involves finding the product of the given functions at \(x = -4\). The correct answer is obtained by substituting the value into the expressions for \(f(x)\) and \(g(x)\) and multiplying the results.

In question 2, finding the expression for \((fg)(x)\) requires using the product of functions formula and substituting the given functions \(f(x)\) and \(g(x)\). The correct answer is determined by multiplying the expressions and simplifying the result.