Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Martin Blake. in South Africa
Mar 10,2025
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\( f \circ g(x) = 6x - 5 \)
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To find \( f \circ g(x) \), we need to substitute \( g(x) \) into \( f(x) \). First, compute \( g(x) \): \[ g(x) = 2x - 3 \] Next, substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] Now use the definition of \( f(x) = 3x + 4 \): \[ f(2x - 3) = 3(2x - 3) + 4 \] Distributing the 3 gives: \[ = 6x - 9 + 4 \] Combining like terms: \[ = 6x - 5 \] So, \( f \circ g(x) = 6x - 5 \).