The function g is defined by
g(x)=2x^2-4 Find g(5x).
g(x)=2x^2-4
so, replacing each x with 5x,
g(5x) = 2(5x)^2-4
Ah, the magnificent function g, always ready to crunch some numbers. Now, let's see what happens when we put g(x) into the magnifier and turn it into g(5x).
We start with g(x) = 2x^2 - 4. Now, we replace every x with 5x and we get:
g(5x) = 2(5x)^2 - 4
Now, let's simplify this expression. The exponent here is 2, so we apply it to both the 5 and the x:
g(5x) = 2(25x^2) - 4
Finally, let's multiply the 2 and the 25:
g(5x) = 50x^2 - 4
Voila! We have successfully transformed g(x) into g(5x)! Just remember to keep an eye on those math monsters. They tend to sneak up on you when you least expect it.
To find g(5x), you need to substitute 5x into the function g(x).
Starting with the original function g(x) = 2x^2 - 4, we substitute 5x for x:
g(5x) = 2(5x)^2 - 4
Next, we simplify 5x^2:
g(5x) = 2(25x^2) - 4
Multiplying the 2 by 25 and combining like terms:
g(5x) = 50x^2 - 4
Therefore, g(5x) = 50x^2 - 4.
To find g(5x), we can substitute 5x into the function g(x).
The function g(x) is defined as g(x) = 2x^2 - 4.
To find g(5x), we substitute 5x into the function in place of x. Let's do that:
g(5x) = 2(5x)^2 - 4
Now, we need to simplify this expression:
First, we square 5x:
(5x)^2 = 25x^2
Now, we substitute this value back into the expression:
g(5x) = 2(25x^2) - 4
Next, we multiply 2 by 25x^2:
2(25x^2) = 50x^2
Now, we substitute this value back into the expression:
g(5x) = 50x^2 - 4
So, g(5x) is equal to 50x^2 - 4.