Inverse function

[opal iron]

yo so

evaluating f^-1 (f(x)) at x=-5

what does that mean

[oblique lynx]

so like it’s a composite function and I need to put f(x) into the inverse

[opal iron]

but specifically at x=-5

so you wanna find f^-1 (f(-5))

[oblique lynx]

yea

But like I’m worried I did part a wrong

which might affect my answer to part b

[opal iron]

well we will find out

so whats f(-5)

[oblique lynx]

48

[opal iron]

ok and then

plug that into your inverse

[oblique lynx]

I got 4

3 sorry*

[opal iron]

mmm hold on

ok so

when you had x/3 = (y+1)^2 when you calculated the inverse

when you square root you need to square root everything

[oblique lynx]

Ok

[opal iron]

and then in square rooting

you need to be careful cuz

it could be either y+1 or -(y+1)

we dont know which right

[oblique lynx]

yea

[opal iron]

but since x < 1

we really want the left side of the inverse

so we wanna take the - version

so sqrt(x/3) = -(y+1)

which gives you a slightly different inverse

[oblique lynx]

Ok

so like

I got this

I divided it by -1 after

[opal iron]

its negative yeah

so its -5

perfec

[oblique lynx]

thank you so much for the help!

is it possible if I could have support with 1 more question though please? It’s to do with the range of a function

[opal iron]

sure

[oblique lynx]

Thanks so it’s q5b

sorry I mean q5a*

[opal iron]

ok so

lets think of it like this

whats the smallest we can make x^2

whats the smallest square number

[oblique lynx]

1

[opal iron]

almost

so theres actually smaller @oblique lynx

0 is the smallest

and then think about, as x gets bigger, does x^2 ever stop growing?

that will tell you the biggest and smallest x^2 can be

[oblique lynx]

It never stops growing

[opal iron]

exactly

so we can say that

x^2 has upper range < infinity

yeah?

[oblique lynx]

Yea

[opal iron]

and then we know x^2 is bigger or eql to 0

so 0 <= x^2 < infty

[oblique lynx]

Yea

[opal iron]

thats the range

[oblique lynx]

ohh okay