Answer:
The domain of g(x) is {xI x > -5} ⇒ first answer
Explanation:
* Lets talk about the transformation at first
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
* lets revise the meaning of the domain
- The domain is all values of x that make the function defined
- Find the values of x which make the function undefined
- The domain will be all the real numbers except those values
* Now we can solve the problem
∵ f(x) = √x
- f(x) translated 5 units to the left, then add x by 5
∴ f(x) ⇒ f(x + 5)
- f(x) translated 3 units up, then add f(x) by 3
∴ f(x) ⇒ f(x) + 3
- The function g(x) is created after the transformation
∴ g(x) = f(x + 5) + 3
∵ f(x) = √x
∴ g(x) = √(x + 5) + 3
- The function will be defined if the value under the square root
is positive (means greater than 0)
∵ The expression under the square root is x + 5
∴ x + 5 > 0 ⇒ subtract 5 from both sides
∴ x > -5
- The domain will be all the real numbers greater than -5
∴ The domain of g(x) is {xI x > -5}