Question

Given f(x)= 2^x and g(x)=x+1, (f*g)(x)

Answer 1

Answer:

x2ˣ + 2ˣ

Step-by-step explanation:

Points to remember

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

It is given that,  f(x)= 2ˣ and g(x)=x+1

To find the value of (f * g)(x)

Let  f(x)= 2ˣ and g(x) = x + 1

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

 =  (2ˣ )* (x + 1)

 = (2ˣ * x) + ( 2ˣ * 1)

  = x2ˣ + 2ˣ

Answer 2

Answer:

$(f\cdot g)(x)=x \cdot 2^x+2^x$

Now if you meant to have an open circle that would lead to a totally different answer. So if that is the case, I need to know. Thank you kindly.

Step-by-step explanation:

$(f\cdot g)(x)=f(x) \cdot g(x)$

$(f\cdot g)(x)=(2^x)\cdot(x+1)$ (Plugging in the given expressions)

$(f\cdot g)(x)=2^x \cdot x+2^x \cdot 1$ (By distributive property)

$(f\cdot g)(x)=x \cdot 2^x+2^x$ (By commutative and identity property)