Question

The function f(x) varies directly with x, and f(x) = 45 when x = 9.

Answer 1

Answer:

Option C = 15

Step-by-step explanation:

In principle when a function f(x) varies directly with x it suggests that any changes in x results in the equivalent changes in f(x). If we have two variables, i.e. y representing f(x) and x representing itself, any increment/decrement in x will result to the same increment/decrement in y by a factor a, thus we can say that y = ax, implying y and x have the same ratio.

In the given question we know that $f(x) = 45$ when $x=9$, which translates as

$f(x=9) = 45$

This tells us that $f(x)$ varies by a factor (lets call it) $a$ for a given value of $x$.

To find this factor we can just divide 45 with 9 which gives: $\frac{45}{9} = 5$

Thus the factor $a$ here is $a=5$ which finally tells us that

$f(x) = 5x$    Eqn (1) our original function.

Since we now know our function we can plug in the value for $x=3$ and solve for $f(x=3)$ as follow:

$f(x=3)= 5*3$

$f(x=3) = 15$

$f(3) = 15$

Looking at the given options in the question we can conclude that the correct answer is Option C = 15