Struggling to solve.

[johngon]

Here is the first problem I'm a bit baffled by:
If f(x)= xsquared -5x+4/x-1, then what is f(-2)

I'm not even quite sure where to begin

 

[Dr.Peterson]

Here is the first problem I'm a bit baffled by:
If f(x)= xsquared -5x+4/x-1, then what is f(-2)

I'm not even quite sure where to begin

You can begin by writing what you mean, carefully. I think you omitted essential parentheses.

What you wrote means [imath]f(x)=x^2-5x+\frac{4}{x}-1[/imath]; what you probably meant is [imath]f(x)=\frac{x^2-5x+4}{x-1}[/imath], which you'd type as f(x) = (x^2-5x+4)/(x-1).

Now, what have you learned about function notation? When we write f(-2), we mean "the value of the expression given for f(x), when x is replaced with -2". For example, if you were told that f(x) = (x-6)/(x+4), then f(-2) = (-2-6)/(-2+4) = -8/2 = -4.

Try doing the same with your example.

 

[Otis]

Hi John. First, a note about notation. When expressing a Rational function using a keyboard, we need to enclose the numerator and denominator within grouping symbols whenever either contains more than a single number/symbol. We use the caret symbol ^ (shift 6, on most manual keyboards) to show exponents.

f(x) = (x^2 - 5x + 4)/(x - 1)

The symbol f(x) is another way of writing the variable y. We call that 'function notation'. Function notation is more useful than 'y' because (1) it allows us to assign different names to different functions and (2) it shows the input inside the parentheses.

The symbol f(-2) represents the function's output when the input is x=-2.

Therefore, symbols x and f(x) are variables. When we have a specific value for x (like -2), the expression f(-2) represents the resulting constant when x=-2.

Begin by substituting x=-2 everywhere x appears in the given function. Then use the Order of Operations to do the arithmetic. The resulting number is the value of f(-2). We call that process of substitution and arithmetic "evaluating function f when x equals -2" or "finding the function's output when the input is -2".

?

 

[johngon]

I wasn't aware of the use of the carat symbol for exponents, so thank you for that, but otherwise, I reproduced the problem exactly as it is posed in an SAT practice question, without the ability to illustrate division with a hard horizontal bar. Still, the answers were helpful if fairly patronizing.

 

[topsquark]

I wasn't aware of the use of the carat symbol for exponents, so thank you for that, but otherwise, I reproduced the problem exactly as it is posed in an SAT practice question, without the ability to illustrate division with a hard horizontal bar.

The mistake in notation x^2-5x+4/x-1 is unfortunately a common one and seen in many textbooks as well as work by professors. However it is critical to know that this notation is not [imath]\dfrac{x^2 - 5x + 4}{x - 1}[/imath]. It is immaterial if it's [imath]x^2-5x+4/x-1[/imath] (with any sized slash) or even [imath]x^2-5x+4 \div x-1[/imath]. Without parentheses this expression is still equal to [imath]x^2 - 5x + \dfrac{4}{x} - 1[/imath] by order of operations

Still, the answers were helpful if fairly patronizing.

I'm not sure why you are saying the answers were patronizing? Why do you think that?

-Dan

 

[canvas]

He doesn't know the definition of function, so why do you guess what's the correct f(x), does it make any sense?