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Help need in P2 plz

i don't know how to do any of these questions

The functions f and g are defined by

f:x -> |x - a|
g:x -> |4x + a|

where 'a' is a positive constant

a) on the same diagram scketch the graphs of f ang g, showing lcearily the coordinates of any points at which your graphs meet the axes

(how can u plot it if u dont even know the value of 'a')

b) use algebra to find, in terms of a, the coordinates of the point at which the graphs of f and g intersect

c) find an expression for fg(x)

d) solve, for x in terms of a, the equation
fg(x)=3a

Thank you
can u follow what i've done?
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i don't know how to do any of these questions

The functions f and g are defined by

f:x -> |x - a|
g:x -> |4x + a|

where 'a' is a positive constant

a) on the same diagram scketch the graphs of f ang g, showing lcearily the coordinates of any points at which your graphs meet the axes

(how can u plot it if u dont even know the value of 'a')

b) use algebra to find, in terms of a, the coordinates of the point at which the graphs of f and g intersect

c) find an expression for fg(x)

d) solve, for x in terms of a, the equation
fg(x)=3a

Thank you


If they intersect, then |4x+a| = |x-a|. This implies either 4x + a = x - a, i.e x = -2a/3, or 4x+a = a-x, i.e x = 0.

f(x) = |x-a| so f(g(x)) = |g(x)-a| = ||4x+a|-a|.

If f(g(x)) = 3a then 3a = ||4x+a|-a|. So 3a = |4x+a| - a so 4a = |4x+a| so x = 3a/4 or -5a/4. You can reject -3a because a is >0.

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