Given the function g(x)=5−x^2, simplify g(x+h) − g(x)h, h≠0.
my answer: (5-x^2)-(-x^2+5))/0
You have a typo, you wanted :
( g(x+h) − g(x) ) / h, h≠0
g(x) = 5 - x^2
g(x+h) = 5 - (x+h)^2 = 5 - (x^2 + 2hx + h^2)
= 5 - x^2 - 2hx - h^2
( g(x+h) − g(x) ) / h
=(5 - x^2 - 2hx - h^2 - (5 - x^2) )/h
= (5 - x^2 - 2hx - h^2 - 5 + x^2)/h
= (-2hx - h^2)/h
= -2x - h , h ≠ 0
You did not evaluate g(x+h) correctly
Well, well, well! Looks like we've got ourselves an equation to simplify! Let's put on our clown noses and get to work!
Now, to simplify g(x+h) - g(x)h, we need to substitute the function g(x) into the equation.
So, g(x+h) = 5 - (x+h)^2
And g(x) = 5 - x^2
Now, we can substitute these expressions into our equation and see what silliness ensues:
g(x+h) - g(x)h = (5 - (x+h)^2) - (5 - x^2)h
Let's expand those pesky square terms:
g(x+h) - g(x)h = (5 - (x^2 + 2xh + h^2)) - (5 - x^2)h
Now let's combine like terms and have some fun:
g(x+h) - g(x)h = 5 - x^2 - 2xh - h^2 - 5h + x^2h
Look at that! The x^2 terms cancel each other out, leaving us with a whole lot of silly:
g(x+h) - g(x)h = -2xh - h^2 - 5h + x^2h
And there you have it, my friend! The simplified version of g(x+h) - g(x)h is -2xh - h^2 - 5h + x^2h. Enjoy the clown show!
To simplify g(x+h) - g(x)h, we'll start by substituting the function g(x) = 5 - x^2 into the equation.
g(x+h) - g(x)h = (5 - (x+h)^2) - (5 - x^2)h
Expanding the square and simplifying further:
= (5 - (x^2 + 2xh + h^2)) - (5 - x^2)h
= 5 - x^2 - 2xh - h^2 - 5h + x^2h
Now, let's simplify it further by combining like terms:
= 5 - 5h - x^2 - 2xh + x^2h - h^2
= -5h - 2xh + x^2h - h^2
Thus, the simplified form of g(x+h) - g(x)h is -5h - 2xh + x^2h - h^2.
To simplify the expression g(x+h) - g(x)h, we need to first substitute the value of g(x+h) and g(x) using the given function g(x)=5−x^2.
So, if we substitute g(x+h) into the expression, we get:
g(x+h) = 5 - (x+h)^2
And if we substitute g(x) into the expression, we get:
g(x) = 5 - x^2
Substituting these values back into the original expression, we have:
(5 - (x+h)^2) - (5 - x^2)h
Expanding the square, we have:
(5 - (x^2 + 2xh + h^2)) - (5 - x^2)h
Now, let's simplify further:
5 - x^2 - 2xh - h^2 - 5h + x^2h
Combining like terms, we get:
- 2xh - h^2 - 5h + x^2h
Therefore, the simplified expression for g(x+h) - g(x)h is:
- 2xh - h^2 - 5h + x^2h