Let f (x) = –5x + 3 and g(x) = 6x – 2, how do you find f • g and its domain?

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Answer 1 · 2016-07-25T17:47:59

$(f*g)(x)=-2(15x^2-14x+3), x in RR$ .

Let $D_f and D_g$ be the domains of the given funs. $f and g$ , resp.

We can easily see that, $D_f=D_g=RR$

Now, by defn. the fun. $f*g$ is defined by, $(f*g)(x)=f(x)*g(x)$ ,

where, $x in D_f nn D_g$ .

Since, $D_f nnD_g=RR$ , we have, #(f*g) : RR rarr RR, where,

$(f*g)(x)=f(x)*g(x)=(-5x+3)(6x-2)=-30x^2+10x+18x-6=-30x^2+28x-6$ .

Thus, $(f*g)(x)=-2(15x^2-14x+3), x in RR$ .