Answer:
Step-by-step explanation:
We can use the definition of inverse functions. Recall that if two functions, <em>f</em> and <em>g</em> are inverses, then:
So, we can let <em>j</em> be the inverse function of <em>h</em>.
Function <em>h</em> is given by:
Find its inverse. Flip variables:
Solve for <em>y. </em>Add:
Hence:
Therefore, <em>a</em> = 1/3 and <em>b</em> = 2/3.
We can verify our solution:
And:
The zero of the function is at 33.69 degree , the graph is plotted and attached with the answer.
<h3>What is a Function ?</h3>A function is a law that relates a dependent variable and an independent variable with each other
It is given that
y = 2tan (x - π/2) +3
To find the zeroes of a function that function has to be equated to zero.
2tan (x - π/2) +3 = 0
2tan (x - π/2) = -3
tan (x - π/2) = -3/2
x - 90 = -56.31
x = 33.69 degree
The zero of the function is at 33.69 degree
For finding the maxima /minima
the derivative is
dy/dx = 2 sec² (x - π/2)
the point at which the slope is zero is substituted in the second derivative to find maxima/minima
d²y/dx² = 4 sec² (x - π/2) tan (x - π/2)
if the value is negative then it is a maxima and if it is positive it is a minima.
The vertical asymptote is found by finding the values that make the function undefined
x = 0+ πn
No horizontal or oblique asymptote
To know more about Function
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