Question

The point (6, 6) is on the graph y = f(x) . Find the corresponding coordinates of this point on the graph y = 4f[1/3x +9] -7

Answer 1

Answer:

Correct answer is:

a. (-9,17)

Step-by-step explanation:

We are given that a point (6, 6) lies on the graph of $y =f(x)$.

Putting the values from the given point:

$6 =f(6)$

That means we are given that $f(6) =6$ ..... (1)

And we have to find the corresponding coordinates of this point on the graph of $y = 4f[\frac{1}3x +9] -7$

From equation (1), we know the value of $f(6)$.

so, let us convert $f[\frac{1}3x +9]$ to a form such that it becomes equal to $f(6)$

$\Rightarrow \dfrac{1}{3}x +9 =6\\\Rightarrow \dfrac{1}{3}x=-3\\\Rightarrow x = -9$

So, let us put $x = -9$ in the given function:

$4f[\frac{1}3\times (-9) +9] -7\\\Rightarrow 4f[-3 +9] -7\\\Rightarrow 4f(6) -7$

Now, using equation (1), putting $f(6)=6$

$\Rightarrow 4\times 6 -7\\\Rightarrow 24-7 \\\Rightarrow y = 17$

Therefore, the point the corresponding point is:

a. (-9,17)