Show that the function f has an inverse by showing that it is strictly monotonic.f(x) = x7 - 3x3 - 9x

What will be an ideal response?


f'(x) = 7x6 - 9x2 - 9 < 0 for all x. Thus, f is monotonic decreasing on the whole real line and so it has an inverse there.

Mathematics

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Find the sum of the series.

A.
B.
C.
D.

Mathematics

Solve the problem.When a tow truck is called, the cost of the service is given by the linear function , where y is in dollars and x is the number of miles the car is towed. Find and interpret the slope of the linear equation.

A. m = 65; The cost of the service increases at a rate of $65 per mile the car is towed. B. m = 65; The number of miles the car is towed increases at a rate of 65 miles per dollar spent on the service. C. m = 3; The cost of the service increases at a rate of $3 per mile the car is towed. D. m = 3; The number of miles the car is towed increases at a rate of 3 miles per dollar spent on the service.

Mathematics

Find the slope and the y-intercept.-x + 10y = 70

A. m = -1; (0, 70)
B. m = ; (0, 7)
C. m = 10; (0, -70)
D. m = - ; (0, 7)

Mathematics

Graph the system of inequalities.2x + 3y ? 6x - y ? 3y ? 2

A.

B.

C.

D.

Mathematics