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Sagot :
The expressions for f(x) and g(x) are:
[tex]\begin{gathered} f\mleft(x\mright)=3x+5 \\ g\mleft(x\mright)=x-1 \end{gathered}[/tex]And we need to determine the following expression:
[tex]f(x)\cdot g(x)[/tex]Step 1. To find f(x)*g(x) we will need to multiply the two functions:
[tex]f(x)\cdot g(x)=(3x+5)(x-1)[/tex]Step 2. To simplify the multiplication, we will use the distributive property:
[tex](a+b)(c+d)=a\cdot c+a\cdot d+b\cdot c+b\cdot d[/tex]Which is to multiply each element of the first parentheses by the two elements in the other parentheses.
Applying the distributive property to our expression:
[tex]f(x)\cdot g(x)=3x\cdot x+3x\cdot(-1)+5\cdot x+5\cdot(-1)[/tex]Step 3. The last step will be to simplify the operations by making the multiplications:
[tex]f(x)\cdot g(x)=3x^2-3x+5x-5[/tex]We can further simplify by combining the terms -3x and +5x into a single term which will be 2x:
[tex]f(x)\cdot g(x)=3x^2+2x-5[/tex]This the equation for f(x)*g(x).
Answer:
[tex]f(x)\cdot g(x)=3x^2+2x-5[/tex]
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