Question

Given a formula
y
=
4
x
+
11
that represents how the values of
x
and
y
vary together.

Define the rule for a function
f
that determines
y
in terms of
x
.

f
(
x
)
=


Solve the equation
y
=
4
x
+
11
for
x
.

x
=


Define the rule for a function
g
that determines
x
in terms of
y
.

g
(
y
)
=


Which of the following are true? Select all that apply.

Answer 1

The function for y in terms of x is:

f(x) = 4x + 11

The function for x in terms of y is:

g(y) = (y - 11)/4.

How to define the rule for the function?

we start with the relation:

y = 4x + 11

And we want a rule:

y = f(x)

Then is trivial to see that:

f(x) = 4x + 11.

That is the rule for the function.

Now we want to fund a function g, that defines x on terms of y, so we need to write:

x = g(y).

To do that, we can isolate x on the given relation:

y = 4x + 11

y - 11 = 4x

(y - 11)/4 = x

Then we have:

x = g(y) = (y - 11)/4

If you want to learn more about functions:

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