We are given:
f(x − 1) = 2x + 3 for all values of x.
We need to find
f(−3).
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Step 1: Understand what we’re being asked.
We want the value of the function f when its input is −3. That is, we want
f(−3).
But the function is defined as
f(x − 1), not directly as f(something). So we need to figure out:
> What value of x makes (x − 1) equal to −3?
Because if we can find that x, then we can plug it into the right-hand side (2x + 3) to get f(−3).
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Step 2: Set up the equation.
We want:
x − 1 = −3
Solve for x:
Add 1 to both sides:
x = −3 + 1
x = −2
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Step 3: Plug this x into the expression for f(x − 1).
Since f(x − 1) = 2x + 3, and when x = −2, then x − 1 = −3, so:
f(−3) = 2*(−2) + 3
= −4 + 3
= −1
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Step 4: Double-check.
Let’s verify:
If x = −2, then x − 1 = −3 → correct.
Then f(−3) = 2*(-2) + 3 = -4 + 3 = -1 → correct.
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Final Answer:
D) −1
Parent Tip: Review the logic above to help your child master the concept of psat math practice worksheet.
