Hello from MrBillDoesMath!
Answer:
The first choice, y = x^3 + 5
Discussion:
Let
y = (x-5) ^ (1/3)
To find the inverse, sway x and y and then solve for y:
x = ( y - 5 )^(1/3) => cube both sides
x^3 = y - 5 => add 5 to both sides
x^3 + 5 = y
So the inverse is x^3 + 5, which is the first choice
Thank you,
MrB
Answer:
The values of x that satisfy the given equation are:
x1 = 1.183 + nπ
x2 = -1.183 + nπ
Step-by-step explanation:
Given tan²x - sin²x/sin²x = 5
Simplifying this, we have
tan²x - 1 = 5
Adding 1 to both sides, we have
tan²x = 6
Because tan²x = (tanx)², we can write as
(tanx)² = 6
Taking square roots of both sides, we have.
tanx = ±√6
x = arctan(±√6) + nπ
≈ 1.183 + nπ or -1.183 + nπ
The angles of all triangles should always sum up to be 180, so knowing this we can solve this problem using the equation x + 3x + 5x - 54 = 180, first we want to combine all our common variables, so we add the x’s together and get 9x - 54 = 180 then we add +54 to both sides so that the x can be by itself and we have 9x = 234, we divide both sides by 9 and get our final answer of x = 26
The asymptote for f(x) is y = 0
Notice the asymptote for g(x) is y = -1, which shift f(x) down 1
apply this to f(x)'s rule: 
Notice the graph of f(x) is shifted right 2 units...this horizontal movement must be applied to the x in f(x)'s rule: 
