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just doing it give me 10 minutes

given f(x) = -x^2 + 4x + 5 x<4

= 2x - 3 x>=4

so now to check for continuous we have to find f(x+) and f( x-)

f( x+) means the value of f(x) where x>=4

f( x -) means the value of f(x) where x <4

f( 4 + ) we have to find so just plug x=4 in f(x) where x>=4

so f( 4+) = -(4)^2 + 4(4) +5

= -16 + 16 +5

f(4+) = 5

now in similer way i will find f (x -) that is f(4 -)

f(4 -) = 2(4) -3

= 8 - 3

= 5

so the value of f( 4+ ) and f( 4-) values are 5

both are same so the given function is continuous

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