If f(x)=2x and g(x)= 1/x, what is the domain of (f*g) (x)
2 answers:
Answer:
The domain of (f*g) (x) is the set of all real numbers; ( -∞, ∞)
Step-by-step explanation:
(f*g) (x) simply means we obtain the product of f(x) and g(x). We are given that;
f(x)=2x
g(x)= 1/x
(f*g) (x) = f(x) * g(x)
(f*g) (x) = 2x * 1/x = 2
This is a horizontal line defined everywhere on the real line. The domain of (f*g) (x) is thus ( -∞, ∞)
Answer:
All real numbers
Step-by-step explanation:
Given : ![f(x)=2x](https://tex.z-dn.net/?f=f%28x%29%3D2x)
![g(x)= \frac{1}{x}](https://tex.z-dn.net/?f=g%28x%29%3D%20%5Cfrac%7B1%7D%7Bx%7D)
To Find : the domain of (f*g) (x)
![f(x)=2x](https://tex.z-dn.net/?f=f%28x%29%3D2x)
![g(x)= \frac{1}{x}](https://tex.z-dn.net/?f=g%28x%29%3D%20%5Cfrac%7B1%7D%7Bx%7D)
![(f\cdot g)(x)=2x \times \frac{1}{x}](https://tex.z-dn.net/?f=%28f%5Ccdot%20g%29%28x%29%3D2x%20%5Ctimes%20%5Cfrac%7B1%7D%7Bx%7D)
![(f\cdot g)(x)=2](https://tex.z-dn.net/?f=%28f%5Ccdot%20g%29%28x%29%3D2)
Since the value of ![(f\cdot g)(x)=2](https://tex.z-dn.net/?f=%28f%5Ccdot%20g%29%28x%29%3D2)
So, the domain of the function is
is all real numbers .
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