Question

The point (3, 6) is on the graph of y= 5f(2(x+3))-4 . Find the original point on the graph of y=f(x).

Answer 1

Answer:

(12, 2) is the original point on the graph of $y=f(x)$.

Step-by-step explanation:

Given:

$y= 5f(2(x+3))-4$ has a point (3, 6) on its graph.

To find:

Original point on graph $y=f(x)$ = ?.

Solution:

We are given that The point (3, 6) is on the graph of $y= 5f(2(x+3))-4$

If we put x = 3 and y = 6 in $y= 5f(2(x+3))-4$, it will satisfy the equation.

Let us the put the values and observe:

$6= 5f(2(3+3))-4\\\Rightarrow 6= 5f(2(6))-4\\\Rightarrow 6= 5f(12)-4\\\Rightarrow 6+4=5f(12)\\\Rightarrow 5f(12)= 6+4\\\Rightarrow 5f(12)= 10\\\Rightarrow f(12)= \dfrac{10}{5}\\\Rightarrow f(12)= 2\\OR\\\Rightarrow 2=f(12)$

Now, let us compare the above with the following:

$y=f(x)$

we get y = 2 and x = 12

So, the original point on graph of $y=f(x)$ is (12, 2).