Questions: f(x)=x+3, g(x)=x^2-3 g(f(x))=?

f(x)=x+3, g(x)=x^2-3 g(f(x))=?
Transcript text: f(x)=x+3, g(x)=x^{2}-3 g(f(x))=?
failed

Solution

failed
failed

Solution Steps

Step 1: Substitute \( f(x) \) into \( g(x) \)

Given \( f(x) = x + 3 \) and \( g(x) = x^2 - 3 \), substitute \( f(x) \) into \( g(x) \): \[ g(f(x)) = g(x + 3) \]

Step 2: Replace \( x \) in \( g(x) \) with \( x + 3 \)

Replace \( x \) in \( g(x) = x^2 - 3 \) with \( x + 3 \): \[ g(x + 3) = (x + 3)^2 - 3 \]

Step 3: Expand \( (x + 3)^2 \)

Expand \( (x + 3)^2 \) using the formula \( (a + b)^2 = a^2 + 2ab + b^2 \): \[ (x + 3)^2 = x^2 + 6x + 9 \]

Step 4: Simplify the expression

Subtract 3 from the expanded expression: \[ g(f(x)) = x^2 + 6x + 9 - 3 = x^2 + 6x + 6 \]

Final Answer

\(\boxed{x^2 + 6x + 6}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
What method does fideism suggest for using reason to test our own beliefs? It does not provide one. Use reason judiciously but keep the faith. Always use reason in all matters of faith.
failedAnswered
d. P(z ≥ -2.5) e. P(-3 < z ≤ 0)
failedAnswered
Find Dot Product A [dot] B.
failedAnswered
QUESTION 7 Consider the following ground state electron configuration: 1s^2 2s^2 2p^4. Which of the ions has this ground state electron configuration? F^-1 N^+1 c^-2 O^-2
failedAnswered
Effect of Price on Demand for Tires Suppose the quantity demanded weekly of the Super Titan radial tires is related to its unit price by the equation [ p+x^2=289 ] where p is measured in dollars and x is measured in units of a thousand. How fast is the quantity demanded weekly changing when x=10, p=189, and the price per tire is increasing at the rate of 2 / week nearest tire.)