anyone know how to solve???

[Sanguinne]

ok so this is the question

f:R-->R, f(x)=mx-4 where m ∈ R\{0}

a) find the x-axis intercept
b)for which values of m is the x-axis intercept less than or equal to 1?
c) find the inverse function of f
d) find the coordinates of the point of intersection of the graph y=f(x) with the graph of y=x
e) find the equation of the line perpendicular to the line at the point with coordinates (0,-4)

[Zealous]

I've got an idea on how to solve most of it, although someone else should probably check with my working, I may not be fully correct.

a)
x-axis intercept,
when







b)
usng values from previous question:


so

c)
for the inverse: swap x and y values






e)
the gradient of the line is
so the gradient of the perpendicular line will be

using the formula

sub in the coordinates:







I'm having a few problems with d though...

[Homer]

ok so this is the question

f:R-->R, f(x)=mx-4 where m ∈ R\{0}

d) find the coordinates of the point of intersection of the graph y=f(x) with the graph of y=x

[Zealous]

How did you get x by itself after equating them?

[KevinooBz]

How did you get x by itself after equating them?

You move mx to the other side and you factorise by taking out x then divide by (1-m).

[Sanguinne]

thanks everyone for ur answers

really helpful