
Concept explainers
To Analyse: The basic functions that inverses of their own.
The basic functions that inverses of their own are
Given:
Determine the basic functions that inverse of their own.
Calculation:
The basic functions which inverses of their own are
Apply the formula for
Replace
Now, apply the formula for
Replace
Thus when
So
Also, if
Apply the formula for
Replace
Simplify the function:
Also,
Replace
Simplify the function:
Hence, when
So,
Chapter 1 Solutions
EBK PRECALCULUS:GRAPHICAL,...-NASTA ED.
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- Consider the function f(x) = 2x³-4x2-x+1. (a) Without doing a sketch, show that the cubic equation has at least one solution on the interval [0,1]. Use a theorem discussed in lectures, or see Section 1.8 of Calculus (7th ed) by Stewart. Ensure that the conditions of the theorem are satisfied (include this in your solution) (b) Now, by sketching the cubic (by hand or by computer), you should see that there is, in fact, exactly one zero in the interval [0,1]. Use Newton's method to find this zero accurate to 3 decimal places. You should include a sketch of the cubic, Newton's iteration formula, and the list of iterates. [Use a computer if possible, e.g., a spreadsheet or MatLab.]arrow_forwardEvaluate the following integrals, showing all your workingarrow_forwardDifferentiate the following functionarrow_forward
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