Michael K. | Math Major Michael works as Engineer and tutors in MathMath Major Michael works as Engineer and...

4.94.9(37 lesson ratings)(37)

1

The trick is to not get caught up in the expression x-1 view it as a number. If the equation said f(3), then wherever you see the x you replace it with the number 3. So f(3) = (3)^2 -5. Now replace the 3 with x-1.

This is one of the confusing things about dealing with functions. The expression that is in the parentheses in f(___) replaces the unknown in the right side of the equation. As in this problem, functions will use the same letter in both places, but they don't represent the same thing!

In f(x-1)=
x^{2} - 5,
the "x" in (x-1) is not the same thing as the "x" in
x^{2} - 5.
Instead, (x-1) is the same as
x.

(Learning this oddity is the point behind having you solve this problem.)

Well, Gene, now you have to give us an example, which will support your very wide point of view. Personally, I like Mike's approach, he gave student an idea and student solved the problem, which is perfect!!!

In given problem,
"x" in the "x^{2} - 5" is the same as "(x - 1)" in "(x - 1)^{2} - 5"
because a function, the rule, is the same for both variables (x) and (x-1).
Same letters - same numbers, or same rules.
If there will be problem like
"if f(x) = x^{2} - 5 , what is g(x-1)?" g(x-1) ? (x-1)^{2} - 5 , because f(x) and g(x) are different functions, unless there will be special condition as f(x) = g(x) .

## Comments

so f(x-1) = (x-1)(x-1)-5

= x^2-2x +1-5

=x^2-2x-4

That's correct. Excellent!!

This is one of the confusing things about dealing with functions. The expression that is in the parentheses in f(___) replaces the unknown in the right side of the equation. As in this problem, functions will use the same letter in both places, but they don't represent the same thing!

In f(

x-1)=x^{2}- 5,the "

x" in (x-1) is not the same thing as the "x" inx^{2}- 5.Instead,

(x-1)is the same asx.(Learning this oddity is the point behind having you solve this problem.)

Gene

Well, Gene, now you have to give us an example, which will support your very wide point of view. Personally, I like Mike's approach, he gave student an idea and student solved the problem, which is perfect!!!

In given problem,

"x" in the "x

^{2}- 5" is the same as "(x - 1)" in "(x - 1)^{2}- 5"because a function,

the rule, is the same for both variables (x) and (x-1).Same letters - same numbers, or same rules.

If there will be problem like

"if f(x) = x

^{2}- 5 , what is g(x-1)?" g(x-1) ? (x-1)^{2}- 5 , because f(x) and g(x) are different functions, unless there will be special condition as f(x) = g(x) .