Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is $(f * g)(x)$ ? $\newline$ $f(x) = 5x$ $\newline$ $g(x) = 3x^2 - 10x$ $\newline$ Write your answer as a polynomial or a rational function in simplest form. $\newline$ ______

View step-by-step help

View step-by-step help

Add and subtract functions

Full solution

Q. What is

(f * g)(x)

?

\newline

f(x) = 5x

\newline

g(x) = 3x^2 - 10x

\newline

Write your answer as a polynomial or a rational function in simplest form.

\newline

______

Identify Formula: Identify the formula for $(f * g)(x)$ . $(f * g)(x)$ is the product of $f(x)$ and $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Multiply Functions: We have: $\newline$ $f(x) = 5x$ $\newline$ $g(x) = 3x^2 - 10x$ $\newline$ Now, we need to multiply these two functions to find $(f * g)(x)$ . $\newline$ $(f * g)(x) = (5x) * (3x^2 - 10x)$
Distribute $5x$ : Distribute $5x$ to each term in $g(x)$ .
$(f \cdot g)(x) = 5x \cdot 3x^2 - 5x \cdot 10x$
Perform Multiplication: Perform the multiplication. $(f \cdot g)(x) = 15x^3 - 50x^2$
Express Answer: Express your answer as a simplified polynomial. $\newline$ The polynomial is already in its simplest form, so no further simplification is needed. $\newline$ $(f * g)(x) = 15x^3 - 50x^2$

More problems from Add and subtract functions

Question

Find the inverse of the function.

y = x + 3

Write your answer in the form

ax + b

. Simplify any fractions.

y =

Posted 5 months ago

Question

(r \circ s)(x)

\newline

3

\newline

2

5

\newline

Write your answer as a polynomial in simplest form.

\newline

(r \circ s)(x) =

Posted 7 months ago

Question

(f + g)(x)

\newline

f(x) = -3x

\newline

g(x) = 3x + 1

\newline

\newline

Write your answer as a polynomial or a rational function in simplest form.

\newline

\underline{\hspace{3cm}}

\newline

Posted 7 months ago

Question

(f * g)(x)

\newline

f(x) = -x + 4

\newline

g(x) = 4x

\newline

\newline

Write your answer as a polynomial or a rational function in simplest form.

\newline

\underline{\hspace{3em}}

\newline

Posted 7 months ago

Question

What is the domain of

\left(\frac{f}{g}\right)(x)

\newline

f(x) = 2x

\newline

g(x) = -5x + 3

\newline

\newline

[\text{A]All real numbers}

\newline

[\text{B]All real numbers except } \frac{3}{5}

\newline

[\text{C]All real numbers except } -\frac{3}{5}

\newline

[\text{D]All real numbers except } \frac{5}{3}

Posted 9 months ago

Question

Find the inverse of the function.

\newline

-3x

\newline

Write your answer in the form

ax + b

. Simplify any fractions.

\newline

Posted 7 months ago

Question

(f \circ g)(0)

\newline

f(x) = 6x

\newline

g(x) = x^2 + 4x

\newline

(f \circ g)(0) =

Posted 7 months ago

Question

(f \circ g)(x)

\newline

f(x) = x^2 + 5

\newline

g(x) = 4x

\newline

Write your answer as a polynomial in simplest form.

\newline

(f \circ g)(x) =

Posted 7 months ago

Question

f(x)

the inverse function of

g(x)

\newline

f(x) = x

\newline

g(x) = -4x

\newline

\newline

\text{[yes]}

\newline

\text{[no]}

Posted 7 months ago

Question

(f * g)(x)

f(x) = 3x^2 + 9x

g(x) = 3x

Write your answer as a polynomial or a rational function in simplest form. ______

Posted 5 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant