Subjects algebra

Composite Function 8Add1E

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1. **State the problem:** Find the value of the composite function $(f \circ g)(-1)$ where $f(x) = 2x - 1$ and $g(x) = x^2 - 3$. 2. **Recall the definition of composite functions:** $$(f \circ g)(x) = f(g(x))$$ This means we first find $g(x)$ and then substitute that result into $f$. 3. **Calculate $g(-1)$:** $$g(-1) = (-1)^2 - 3 = 1 - 3 = -2$$ 4. **Substitute $g(-1)$ into $f$:** $$f(g(-1)) = f(-2) = 2(-2) - 1 = -4 - 1 = -5$$ 5. **Final answer:** $$(f \circ g)(-1) = -5$$ The correct choice is A: -5.