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f(x)=3x-2

g(x)=x+3
find (f × g)(x)
a)3x^2+7x-6
b)3x^2-6
c)3x^3+7x^2-6x
d)3x^2+11x-6

1 answer

To find \((f \times g)(x)\), we need to multiply the functions \(f(x)\) and \(g(x)\):

  1. Given: \[ f(x) = 3x - 2 \] \[ g(x) = x + 3 \]

  2. Now, calculate \((f \times g)(x) = f(x) \cdot g(x)\): \[ (f \times g)(x) = (3x - 2)(x + 3) \]

  3. Expand the expression using the distributive property (FOIL): \[ = 3x \cdot x + 3x \cdot 3 - 2 \cdot x - 2 \cdot 3 \] \[ = 3x^2 + 9x - 2x - 6 \]

  4. Combine like terms: \[ = 3x^2 + (9x - 2x) - 6 \] \[ = 3x^2 + 7x - 6 \]

Thus, \((f \times g)(x) = 3x^2 + 7x - 6\).

So, the answer is: a) \(3x^2 + 7x - 6\).