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Unformatted text preview: , ) nd a formula for f-1 . g) If f ( t ) = e 18 t 3-12 , nd f-1 (1). h) For what values of k does the equation log 5 (6 x 2 + 3) = k have no solution. i) Expand the expression log 4 x 6 y 5 ( x + y ) 8 into one that contains several simpler loga-rithms. 2. Questions on unit-step functions (Heaviside functions). a) Express the piecewise dened functions in terms of unit-step functions and draw the graph of each function. i) f ( x ) = 1 , x < 2-x, < x < 2 2 , x > 2 ii) f ( x ) = b sin x, x < 2 + 2 cos x, x > iii) f ( x ) = , x <-1 x-2 ,-1 < x < 3 x-4 , 3 < x < 5 , x > 5 b) Draw the graph of the given functions i) f ( x ) = h ( x 2-1) ii) f ( x ) = 5 h (4-x 2 ) 3. Questions on hyperbolic functions . a) Evalutate 3 cosh1 b) Show that sinh-1 ( x ) = ln p x + r x 2 + 1 P 2...
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