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-Exponential and Logarithmic Functions- Write a function rule representing the following.

-Exponential and Logarithmic Functions- Write a function rule representing the following-example-1
User Slavo
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Given functions:


f(x)=2x^2-1
g(x)=-5x

The problem is asking for a multiplication of the functions, which can be done as follows:


(fg)(x)=f(x)* g(x)

Then, we have to multiply the functions:


(fg)(x)=(2x^2-1)*(-5x)

Simplifying we get:


(fg)(x)=(2x^2\cdot-5x)-(1\cdot-5x)
(fg)(x)=-10x^3+5x

In the second question, the problem is asking for a composition, which is equal to the following:


(g\circ f)(x)=g(f(x))

Then, in this case, we have to replace all the x in g(x) function by f(x):


(g\circ f)(x)=-5\cdot(2x^2-1)

Simplifying:


(g\circ f)(x)=-10x^2+5

Answer:


(fg)(x)=-10x^3+5x
(g\circ f)(x)=-10x^2+5

User Kaushik Thanki
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