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<h3>A.</h3>
See below for a graph
<h3>B.</h3>The inverse of a function appears on a graph as the reflection of the function across the line y=x. This is because the inverse relation is effectively the same relation with the variables x and y swapped. Here, the graphs of f(x) and g(x) are mirror images of each other across the line y=x, so we can see they are inverse functions.
The same technology allows us to graph y=f(g(x)) and y=g(f(x)). Both are graphs of y=x, as expected.
Answer:
The domain is {x : x ∈ R} or (-∞ , ∞)
Step-by-step explanation:
* Lets explain how to find the domain
- The domain of the function is the values of x which make the
function defined
- The quantity under the square root must be ≥ 0 because there is
no square root for negative value
* Lets solve the problem
∵ f(x) = √(x² - x + 6)
∴ The value of (x² - x + 6) must be greater than or equal zero because
there is no square root for negative value
- Graph the function to know which values of x make the quantity
under the root is negative that means the values of x which make
the graph under the x-axis
∵ The graph doesn't intersect the x-axis at any point
∵ All the graph is above the x-axis
∴ There is no value of x make f(x) < 0
∴ x can be any real number
∴ The domain of f(x) is all real numbers
∴ The domain is {x : x ∈ R} or (-∞ , ∞)
