Question

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18. [-/4.8 Points]
DETAILS
LARPCALCLIM5 1.9.047.
Consider the following function.
f(x) = 25 - x2, 0 < x<5
(a) Find the inverse function of f.
f 1(x) =
,0 3 x<
(b) Graph both f and flon the same set of coordinate axes.
y
y
6
4
4
- x
6
-6
-4
-2
2
4
-6
-4
-2
2
4
6
y
y
6
6
4
-6
-4
2
6
-6
-4
-2
4
6
(c) Describe the relationship between the graphs of f and f1
O The graph of f1is the reflection of fin the y-axis.
0 The graph of f-1
is the reflection of f in the line y = -X.
O The graph of f is the same as the graph of f.
O The graph of F1 is the reflection of f in the X-axis.
(d) State the domain and range of f. (Enter your answers using interval notation.)
dormain
range
State the domain and range of f-1 (Enter your answers using interval notation.)
domain
range

20. [-14.8 Points]
DETAILS
LARPCALCLIM5 1.10.062.
Use Hooke's Law, which states that the distance a spring stretches (or compresses) from its natural, or equilibrium, length varies directly as the applied force on the spring.
A force of 265 newtons stretches a spring 0.15 meter.
(a) What force stretches the spring 0.4 meter? (Round your answer to two decimal places.)
N
(b) How far does a force of 140 newtons stretch the spring? (Round your answer to two decimal places.)
m

22. [-14.8 Points]
DETAILS
LARPCALCLIM5 1.10.051.EP.
Consider the following statement.
y varies inversely as X.
Find a mathematical model that represents the statement. (Let k be the constant of proportionality.)
If y = 2 when x = 24 and it is known thaty varies inversely as X, find the value of the constant of proportionality.
k =
Find a mathematical model in terms of x and y that represents the statement when y = 2 and x = 24.

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