Given f(x)= -6+x^2, find values of f(x+1), f(x) - f(7)

[Gadsilla]

I'm unsure how I'd start on this. Initially I just added the given function with the values:

f(x)=(-6+x^2)(x+1)
f(x)+f(-7)(-6+x^2)

However, I'm pretty sure that I am doing something wrong.

 

[stapel]

I'm unsure how I'd start on this. Initially I just added the given function with the values:

f(x)=(-6+x^2)(x+1)
f(x)+f(-7)(-6+x^2)

However, I'm pretty sure that I am doing something wrong.

View attachment 10455

The function-notation rule says to take whatever is the input, and plug it in for x in the formula. So:

. . . . .f(x) = 2x; f(3) = 6; f(0) = 0; f(@) = 2@

In your case, you need to plug "x + 1" in for every instance of x in the rule:

. . . . .f(x) = -6 + x^2

. . . . .f(x + 1) = -6 + [x + 1]^2 = -6 + x^2 + 2x + 1

...and so forth. Follow this standard methodology to get your final answers.

 

[Gadsilla]

The function-notation rule says to take whatever is the input, and plug it in for x in the formula. So:

. . . . .f(x) = 2x; f(3) = 6; f(0) = 0; f(@) = 2@

In your case, you need to plug "x + 1" in for every instance of x in the rule:

. . . . .f(x) = -6 + x^2

. . . . .f(x + 1) = -6 + [x + 1]^2 = -6 + x^2 + 2x + 1

...and so forth. Follow this standard methodology to get your final answers.

''f(x + 1) = -6 + [x + 1]^2 = -6 + x^2 + 2x + 1'' That doesn't make complete sense to me. Why is it ''-6+[x+1]^2='' why is there an ^2 at the end ?

 

[sinx]

''f(x + 1) = -6 + [x + 1]^2 = -6 + x^2 + 2x + 1'' That doesn't make complete sense to me. Why is it ''-6+[x+1]^2='' why is there an ^2 at the end ?

f(x)=-6+x²
f(x+1)=-6+(x+1)²

 

[mmm4444bot]

Given f(x)= -6+x^2, find … f(x+1)

… Initially I [did this]:

(-6+x^2)(x+1) …

This makes me think that you're reading the notation f(x+1) as though it means f times (x+1).

f(x+1) does not indicate multiplication. It's a special notation known as 'function notation'. Check your textbook's index or use Google, to learn about this notation. It is a very important notation to understand because it's used so much in math.

Let us know, if you see something in those lessons that you're still unsure about. :cool:

 

[Gadsilla]

This makes me think that you're reading the notation f(x+1) as though it means f times (x+1).

f(x+1) does not indicate multiplication. It's a special notation known as 'function notation'. Check your textbook's index or use Google, to learn about this notation. It is a very important notation to understand because it's used so much in math.

Let us know, if you see something in those lessons that you're still unsure about. :cool:

Thank you. That's how I read it. I went from 4 years with no math to calculus so I make a lot of stupid mistakes and forgot A LOT of things.