How do you determine #h(x)=f(x)g(x)# and #k(x)=f(x)/g(x)# given #f(x)=2x-1# and #g(x)=3x+4#?

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Answer 1 · 2017-06-01T14:01:50

#h(x) = 6 x^(2) + 5 x - 4#

#"and"#

#k(x) = frac(2 x - 1)(3 x + 4)#

First, let's evaluate #h(x) = f(x) g(x)#.

Let's substitute the expressions for #f(x)# and #g(x)#:

#Rightarrow h(x) = (2 x - 1)(3 x + 4)#

#Rightarrow h(x) = (2 x)(3 x) + (2 x)(4) + (- 1)(3 x) + (- 1)(4)#

#Rightarrow h(x) = 6 x^(2) + 8 x - 3 x - 4#

#Rightarrow h(x) = 6 x^(2) + 5 x - 4#

Then, let's evaluate #k(x) = frac(f(x))(g(x))#.

We will do the same thing as before and substitute the expressions:

#Rightarrow k(x) = frac(2 x - 1)(3 x + 4)#

Therefore, #h(x) = 6 x^(2) + 5 x - 4# and #k(x) = frac(2 x - 1)(3 x + 4)#.